Don Balon say the Gunners would be prepared to accept a deal worth £85m for the Chilean superstar in the summer.
Real are extremely interested in Sanchez and they might have an ace up their sleeve to get the deal done at a cut-price fee.
The report claims they could use Alvaro Morata as a makeweight in the deal to make up almost half of Arsenal's asking price.
Real are thought to want around £40m for Morata, meaning the forward - plus £45m - could be enough to do a deal with the Gunners this summer.
Sanchez is frustrated at Arsenal's inability to seriously challenge for top titles.
He is holding out over a new contract and his current deal has less than 16 months left to run.
He wants close to £300,000-a-week to stay but Arsenal appear reluctant to meet those demands and they're offering closer to £200,000-a-week.
The stalemate could force Arsenal to sell in the summer or risk losing him for nothing in 2018.